Geodesic
On cyclic Descents for Tableaux
Séminaire lotharingien de combinatoire, 80B (2018) 
Ron M. Adin; Victor Reiner,; Yuval Roichman. On cyclic Descents for Tableaux. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a59/
@article{SLC_2018_80B_a59,
     author = {Ron M. Adin and Victor Reiner, and Yuval Roichman},
     title = {On cyclic {Descents} for {Tableaux}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a59/}
}
TY  - JOUR
AU  - Ron M. Adin
AU  - Victor Reiner,
AU  - Yuval Roichman
TI  - On cyclic Descents for Tableaux
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a59/
ID  - SLC_2018_80B_a59
ER  - 
%0 Journal Article
%A Ron M. Adin
%A Victor Reiner,
%A Yuval Roichman
%T On cyclic Descents for Tableaux
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a59/
%F SLC_2018_80B_a59

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

The notion of descent set, for permutations as well as for standard Young tableaux (SYT), is classical. Cellini introduced a natural notion of cyclic descent set for permutations, and Rhoades introduced such a notion for SYT - but only for rectangular shapes. In this work we define cyclic extensions of descent sets in a general context, and prove existence and essential uniqueness for SYT of almost all shapes. The proof applies nonnegativity properties of Postnikov's toric Schur polynomials, providing a new interpretation of certain Gromov-Witten invariants.